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Unformatted text preview: Assignment 5 – ACTSC 433/833, Winter 2012 (Due at the beginning of the class on March 29) For this assignment, if needed, you can use any software such as Maple, Mathe matica, and MATLAB to find roots of an equation. 1. A onecovariate Cox proportional hazards model of h ( x ) = h ( x ) e βZ is used to study losses from two lines of business. Line 1 has Z = 0 and line 2 has Z = 1. A sample of size five is taken from each line. Line 1 : 135 , 160 , 240 , 320 , 380 . Line 2 : 115 , 140 , 205 , 245 , 285 . The baseline survival function is S ( x ) = 100 x α , x > 100 , α > 0. (a) Determine the maximum likelihood estimates of α and β . [10 marks] (b) Determine the maximum likelihood estimate for the median loss in line 1. [4 marks] (c) Determine the maximum likelihood estimate for the mean loss in line 2. [4 marks] (d) Determine the maximum likelihood estimate for the probability that a loss in line 2 will exceed 200. [2 marks] 2. Repeat Question 1 using a different baseline survival function, namely, assume that a2....
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 Winter '09
 johnny
 Maximum likelihood, class a, maximum likelihood estimate, Survival analysis

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